- The Following Diagram Shows The Potential Energy Function For A Harmonic Oscillator Where U X Bx2 And B Is A Real Cons 1 (186.93 KiB) Viewed 29 times
The following diagram shows the potential energy function for a harmonic oscillator: where U(x)=bx2 and b is a real constant. (a) Write down the time independent Schrödinger equation, TISE, that applies to the harmonic oscillator with this form of the potential. (b) Show that the following wavefunction is a suitable solution to the TISE: ψ1(x)=C1e−αx2 where C1 is a normalization constant and α is real. (c) Find an expression for the energy E in terms of α and other constants. (d) Find an expression for α in terms of b and other constants. (e) Does this wavefunction have even or odd parity? Explain briefly. (f) Find the normalization condition for this wavefunction. You may find the following information useful: ∫−∞∞xne−ax2dx=0 for n odd ∫−∞∞x2me−ax2dx=2mam1.3.5…(2 m−1)aπ